SOLUTION: Simplify the square root of 1215

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Question 849806: Simplify the square root of 1215
Answer by jim_thompson5910(35256) About Me  (Show Source):
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Solved by pluggable solver: Simplifying Square Roots (whole numbers only)
sqrt%281215%29 Start with the given expression


The goal of simplifying expressions with square roots is to factor the radicand into a product of two numbers. One of these two numbers must be a perfect square. When you take the square root of this perfect square, you will get a rational number.

So let's list the factors of 1215

Factors:

1, 3, 5, 9, 15, 27, 45, 81, 135, 243, 405, 1215



Notice how 81 is the largest perfect square, so lets factor 1215 into 81*15





sqrt%2881%2A15%29 Factor 1215 into 81*15



sqrt%2881%29%2Asqrt%2815%29 Break up the square roots using the identity sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29



9%2Asqrt%2815%29 Take the square root of the perfect square 81 to get 9



So the expression sqrt%281215%29 simplifies to 9%2Asqrt%2815%29



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Check:

Notice if we evaluate the square root of 1215 with a calculator we get


sqrt%281215%29=34.8568501158667


and if we evaluate 9%2Asqrt%2815%29 we get


9%2Asqrt%2815%29=34.8568501158667


This shows that sqrt%281215%29=9%2Asqrt%2815%29. So this verifies our answer